New Ratio Estimators for Population Mean under Unequal Probability Sampling Without Replacement in the Presence of Missing Data: A Case Study on Fine Particulate Matter in Bangkok, Thailand

Abstract

Missing data are frequently present in datasets and give rise to a myriad of issues that significantly affect data utilization. The missing data needs to be handled before data can be efficiently estimated and applied. New ratio estimators for population mean were proposed for use when data are missing completely at random and for a more flexible situation where missing data are missing at random in the study variable under unequal probability sampling without replacement. Furthermore, the variance estimators of the proposed ratio estimators were investigated under a reverse framework.  We show theoretically that the proposed estimators were approximately unbiased estimators. The proposed estimators were utilized in simulation studies and were applied to the study of fine particulate matter data in Suan Luang District, Bangkok, Thailand in order to see how the proposed estimators performed. The results from the application to fine particulate matter showed that the ratio estimators and their variance estimators worked better than existing estimators, producing less estimated variances. Therefore, they could be applied to estimate the average fine particulate matter even when missing values appeared.